Phonon polariton

A phonon polariton is a normal mode mixing an electromagnetic field with a polar optical lattice vibration. In a lossless isotropic oscillator model, $c^2{k}^2={\omega }^2{ϵ}_{\infty }({\omega }_{\mathrm{LO}}^2-{\omega }^2)/({\omega }_{\mathrm{TO}}^2-{\omega }^2)$. With $u=c^2{k}^2/{ϵ}_{\infty }$, its two transverse branches obey ${\omega }_{\pm }^2=[{\omega }_{\mathrm{LO}}^2+u\pm \sqrt{({\omega }_{\mathrm{LO}}^2+u{)}^2-4u{\omega }_{\mathrm{TO}}^2}]/2$. The nearly flat longitudinal optical mode is distinct from the upper transverse branch.